Energy balance worksheet with answers

Free printable Energy balance worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Heaterwater · 20 °C45 °CQ = ?

A stream of water flowing at 5 kg/s is heated from 20 °C to 45 °C. Find the heat duty Q.

ṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tin = 20 °CTout = 45 °C
Q = kW
2.Easy
Heaterwater · 35 °C85 °CQ = ?

A stream of water flowing at 1 kg/s is heated from 35 °C to 85 °C. Find the heat duty Q.

ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tin = 35 °CTout = 85 °C
Q = kW
3.Medium
hot sidecold sideethanol · 160 °C100 °Cwater · 25 °Ct = ? °C

Hot ethanol cools water in a counter-flow heat exchanger with no heat loss. Find the water outlet temperature tout.

ṁh = 2 kg/scp,h = 2.44 kJ/(kg·K)Th: 160 → 100 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)tin = 25 °C
tout = °C
4.Medium
hot sidecold sidelight oil · 180 °C140 °Cwater · 30 °Ct = ? °C

Hot light oil cools water in a counter-flow heat exchanger with no heat loss. Find the water outlet temperature tout.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 140 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)tin = 30 °C
tout = °C
5.Hard
hot sidecold sidelight oil · 180 °C60 °Cwater · 15 °C50 °C · ṁ = ?5% lost

Hot light oil heats water in an exchanger that loses 5% of the heat released by the hot stream to the surroundings. Find the water flow rate ṁc needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 60 °Ct: 15 → 50 °Ccp,c = 4.18 kJ/(kg·K)loss = 5 %
ṁc = kg/s
6.Hard
hot sidecold sideethanol · 130 °C60 °Cwater · 15 °C50 °C · ṁ = ?15% lost

Hot ethanol heats water in an exchanger that loses 15% of the heat released by the hot stream to the surroundings. Find the water flow rate ṁc needed.

ṁh = 1 kg/scp,h = 2.44 kJ/(kg·K)Th: 130 → 60 °Ct: 15 → 50 °Ccp,c = 4.18 kJ/(kg·K)loss = 15 %
ṁc = kg/s

Answer key

  1. 1. Q = 522.5 kW
  2. 2. Q = 209 kW
  3. 3. tout = 48.35 °C
  4. 4. tout = 35.02 °C
  5. 5. ṁc = 0.8182 kg/s
  6. 6. ṁc = 0.9923 kg/s

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